Formation of stable solitons in quadratic nonlinear media

Abstract

Dispersive quadratic media with wave mixing between the first- and second-harmonic modes due to a ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ nonlinearity are shown to inhibit wave collapse and to support stable solitons. The stability of this coupled-soliton family is demonstrated by means of a Lyapunov analysis based on the energy integral of the wave-coupling equations. The dynamics of the coupled modes is finally studied using a virial identity, which predicts either a stable propagation of the mutually trapped solitons or a spreading of both waves, depending on the incident-beam power.